# What is the sum of the measures of the interior angles of an octagon?

Sep 8, 2016

${1080}^{\circ}$

#### Explanation:

To calculate the $\textcolor{b l u e}{\text{sum of the interior angles of a polygon}}$ in general use.

$\textcolor{red}{\overline{\underline{| \textcolor{w h i t e}{\frac{a}{a}} \textcolor{b l a c k}{{180}^{\circ} \left(n - 2\right)} \textcolor{w h i t e}{\frac{a}{a}} |}}}$
where n represents the number of sides of the polygon.

For an octagon with 8 sides, n = 8

$\Rightarrow \text{sum of interior angles} = {180}^{\circ} \times \left(8 - 2\right)$

$= {180}^{\circ} \times 6 = {1080}^{\circ}$